Rationalize the denominator of 3√2/3√2-2√3

1.	Rationalize the denominator of 3√2/3√2-2√3
Answer» Answer : = 3 + √6 Step-by-step explanation : $\underline{\underline{\bf <klux>RATIONALIZING</klux> \ factor:}}$ $\bigstar$ The factor of multiplication by which rationalization is done, is CALLED as rationalizing factor. $\bigstar$ If the product of two surds is a RATIONAL NUMBER, then each surd is a rationalizing factor to other. $\bigstar$ For EXAMPLE, rationalizing factor of (3 + √2) is (3 - √2) ___________________________ $\bf =\frac{3\sqrt{2}}{3\sqrt{2}-2\sqrt{3}}$ Rationalizing factor = 3√2 + 2√3 $\bf =\frac{3\sqrt{2}}{3\sqrt{2}-2\sqrt{3}} \times \frac{3\sqrt{2}+2\sqrt{3}}{3\sqrt{2}+2\sqrt{3}} \\\\\\ =\frac{3\sqrt{2}(3\sqrt{2}+2\sqrt{3})}{(3\sqrt{2}-2\sqrt{3})(3\sqrt{2}+2\sqrt{3})} \\\\\\ =\frac{9(\sqrt{2})^2+6\sqrt{6}}{(3\sqrt{2})^2-(2\sqrt{3})^2} \\\\\\ =\frac{9(2)+6\sqrt{6}}{9(2)-4(3)} \\\\\\ =\frac{18+6\sqrt{6}}{18-12} \\\\\\ =\frac{6(3+\sqrt{6})}{6} \\\\\\ =3+\sqrt{6}$

Answer»

Answer :

= 3 + √6

Step-by-step explanation :

$\underline{\underline{\bf <klux>RATIONALIZING</klux> \ factor:}}$

$\bigstar$ The factor of multiplication by which rationalization is done, is CALLED as rationalizing factor.

$\bigstar$ If the product of two surds is a RATIONAL NUMBER, then each surd is a rationalizing factor to other.

$\bigstar$ For EXAMPLE, rationalizing factor of (3 + √2) is (3 - √2)

___________________________

$\bf =\frac{3\sqrt{2}}{3\sqrt{2}-2\sqrt{3}}$

Rationalizing factor = 3√2 + 2√3

$\bf =\frac{3\sqrt{2}}{3\sqrt{2}-2\sqrt{3}} \times \frac{3\sqrt{2}+2\sqrt{3}}{3\sqrt{2}+2\sqrt{3}} \\\\\\ =\frac{3\sqrt{2}(3\sqrt{2}+2\sqrt{3})}{(3\sqrt{2}-2\sqrt{3})(3\sqrt{2}+2\sqrt{3})} \\\\\\ =\frac{9(\sqrt{2})^2+6\sqrt{6}}{(3\sqrt{2})^2-(2\sqrt{3})^2} \\\\\\ =\frac{9(2)+6\sqrt{6}}{9(2)-4(3)} \\\\\\ =\frac{18+6\sqrt{6}}{18-12} \\\\\\ =\frac{6(3+\sqrt{6})}{6} \\\\\\ =3+\sqrt{6}$